The coronavirus disease 2019 (COVID-19) pandemic has changed the lifestyles of individuals all over the world, induced a fear of virus transmission and confusion, and brought about many other potentially devastating psychological impacts. To minimize the spread of COVID-19, governments all over the world have implemented various practices including lockdowns, home quarantines, spatial distancing, and online teaching within schools, colleges, and/or universities. The present cross-sectional study was carried out to investigate the associations between socio-demographic factors and fear of COVID-19 among undergraduate and postgraduate students in public universities Lahore, Pakistan. Data were collected utilizing an online Google Forms survey based on a convenience sample of 397 undergraduate and postgraduate students of public universities (78% female; mean age = 24 years), enrolled in the subject of education (54%) and psychology (46%) when the virus was spreading rapidly throughout Pakistan. All the participants completed the Fear of COVID-19 Scale and questions concerning socio-demographic variables. Results indicated that the fear of COVID-19 was higher among the education students and female students. Fear of COVID-19 (i.e., scores on the FCV-19S) was positively associated with the participants’ personal or family history of illness and number of deaths in family. The level of fear of COVID-19 was different among the students who had physical illness, psychological illness, and no any history of illness personally or in their family.